It is well known that in turbulent fluids, small random perturbations can
produce relevant macroscopic effects. By this reason, the incorporation of a
stochastic white noise force in the Navier-Stokes equations [1]} is
widely recognized as an important step to understand the turbulence
phenomena. In this perspective, we can find in [2]} (see Lemma 2.2) a
deduction of stochastic Navier-Stokes equations from fundamental principles,
by showing that the stochastic Navier-Stokes equations are a real physical
model. Nowadays, the stochastic Navier-Stokes equations are quite well
understood, see for instance in [3]}, [4]}, [5]}, [6]} and the references therein. In spite of that, there are few results in
the literature about stochastic non-Newtonian fluids [7]}, [8]}, [9]}, [10]}. In this paper we consider the stochastic second
grade equations with multiplicative noise given by
\(\left\lbrace \begin{array}{l}\tfrac{\partial }{\partial t}\left( Y-\alpha \Delta Y\right) =\nu \Delta Y-\mathrm {curl}\left( Y-\alpha \Delta Y\right) \times Y-\nabla \pi +U+G(t,Y)\,\dot{W}_{t},\vspace{5.69054pt} \\\mathrm {div}\,Y=0\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \text{in }\mathcal {O}\times (0,T),\vspace{5.69054pt}\end{array}\right. \) 
